Difference between revisions of "Ground Source Heat Pump"
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The governing equation is: | The governing equation is: | ||
| − | [[File:TDequation.png|frameless|left]] | + | [[File:TDequation.png|frameless|left]]<br style="clear:both;" /> |
| + | where T(x,τ) is the sub-soil temperature at depth x metres and after τ days | ||
| − | + | ''erf''() is the Gauss error function; conveniently, this function is supported for MS Excel spreadsheets as =ERF() | |
and for this case study the following values were used: | and for this case study the following values were used: | ||
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T<sub>i</sub> = 10°C, the initial, uniform temperature throughout the ground | T<sub>i</sub> = 10°C, the initial, uniform temperature throughout the ground | ||
| − | α = 0.0647 m²/day the Thermal Diffusivity for "Coal Measures Group" geology | + | α = 0.0647 m²/day the Thermal Diffusivity for "Coal Measures Group" geology (GeoReports, British Geological Survey) |
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| + | Additionally, the house is on a 12 metre x 18 metre plot and has a heating requirement of 12,000 kW-h per year equivalent to the OFGEM Typical Domestic Consumption Value (TDCV) for ''gas'', for a medium size household (the GSHP is providing space heating and domestic hot water in place of a gas boiler). The case study covers an eight month 'heating season' from October to May | ||
Revision as of 13:02, 27 November 2019
GSHP in a suburban setting - a case study
In the following scenario an early adopter installs a Ground Source Heat Pump (GSHP) and initially enjoys uncontended use of the sensible heat contained within a hemispherical volume of sub-soil beneath her - and her neighbours' properties. Later, under a policy of mass adoption of GSHP technology, all the surrounding properties are competing for the same heat and the effective source volume is bounded by the area of property, straight down.
This latter case can be mathematically modelled as "Transient Heat Conduction in a Semi-infinite Solid". The housing estate is an infinite surface plane, held at the heat extraction temperature T0°C. The ground extends to an infinite distance in all horizontal directions - and downward (hence semi-infinite solid) and is initially at a uniform temperature Ti°C. Since Ti > T0 heat flows from below ground towards the surface where it is collected by the slinky coils and used to heat the house. The mathematical solution (proof not given here) provides equations for the temperature distribution within the sub-soil, as a function of time and depth and the heat flux, that is the quantity of heat that can be extracted at the surface, a function of time alone
Temperature distribution
The governing equation is:
where T(x,τ) is the sub-soil temperature at depth x metres and after τ days
erf() is the Gauss error function; conveniently, this function is supported for MS Excel spreadsheets as =ERF()
and for this case study the following values were used:
T0 = 5°C, the temperature at which heat is being extracted
Ti = 10°C, the initial, uniform temperature throughout the ground
α = 0.0647 m²/day the Thermal Diffusivity for "Coal Measures Group" geology (GeoReports, British Geological Survey)
Additionally, the house is on a 12 metre x 18 metre plot and has a heating requirement of 12,000 kW-h per year equivalent to the OFGEM Typical Domestic Consumption Value (TDCV) for gas, for a medium size household (the GSHP is providing space heating and domestic hot water in place of a gas boiler). The case study covers an eight month 'heating season' from October to May